Average Error: 0.0 → 0.0
Time: 1.1m
Precision: 64
\[x + \left(y - z\right) \cdot \left(t - x\right)\]
↓
\[\mathsf{fma}\left(t - x, y - z, x\right)\]
x + \left(y - z\right) \cdot \left(t - x\right)
↓
\mathsf{fma}\left(t - x, y - z, x\right)
double f(double x, double y, double z, double t) {
        double r22539398 = x;
        double r22539399 = y;
        double r22539400 = z;
        double r22539401 = r22539399 - r22539400;
        double r22539402 = t;
        double r22539403 = r22539402 - r22539398;
        double r22539404 = r22539401 * r22539403;
        double r22539405 = r22539398 + r22539404;
        return r22539405;
}
↓
double f(double x, double y, double z, double t) {
        double r22539406 = t;
        double r22539407 = x;
        double r22539408 = r22539406 - r22539407;
        double r22539409 = y;
        double r22539410 = z;
        double r22539411 = r22539409 - r22539410;
        double r22539412 = fma(r22539408, r22539411, r22539407);
        return r22539412;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Target

Original0.0
Target0.0
Herbie0.0
\[x + \left(t \cdot \left(y - z\right) + \left(-x\right) \cdot \left(y - z\right)\right)\]

Derivation

  1. Initial program 0.0

    \[x + \left(y - z\right) \cdot \left(t - x\right)\]

  2. Simplified0.0

    \[\leadsto \color{blue}{\mathsf{fma}\left(t - x, y - z, x\right)}\]

  3. Final simplification0.0

    \[\leadsto \mathsf{fma}\left(t - x, y - z, x\right)\]

Reproduce

herbie shell --seed 2019200 +o rules:numerics
(FPCore (x y z t)
  :name "Data.Metrics.Snapshot:quantile from metrics-0.3.0.2"

  :herbie-target
  (+ x (+ (* t (- y z)) (* (- x) (- y z))))

  (+ x (* (- y z) (- t x))))